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Proof step 357 from proof inv-write_inode (previous step)

afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), synced(files, icache, pcache), m ∈ files ⊦ synced(files[m, (files[m].meta:= md).size:= m2], icache, pcache), m ∈ icache

Heuristic use patterns applied rule insert rewrite lemma

And obtained the following new goals

Proof step 358:
⊦ synced(files, icache, pcache) → (¬ synced(files0, icache0, pcache0) ↔ ¬(∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0)))
Proof step 359:
afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), synced(files, icache, pcache), m ∈ files ⊦ m ∈ icache, ∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files[m, (files[m].meta:= md).size:= m2] → synced(ino, icache, pcache)

Rule argument

spec: cache-base name: synced-files-variant1 seq: ⊦ synced(files, icache, pcache) → ( ¬ synced(files0, icache0, pcache0) ↔ ¬ (∀ ino. (ino ∈ files → synced(ino, icache, pcache)) → ino ∈ files0 → synced(ino, icache0, pcache0))) subst: [files, icache, pcache, files0, icache0, pcache0] → [files, icache, pcache, files[m, (files[m].meta:= md).size:= m2], icache, pcache] flags: <all paths>

Additional information

Used terms: files, icache, pcache, files[m, (files[m].meta:= md).size:= m2], icache, pcache